I have guessed that the extrema point will be a point such that x=5y+2z and tried solving for the curve of intersection of z=(x-5y)/2 and the constraint x+15y+7z=44 and finding the max of the curve of intersection that results but is unfamiliar with the techniques involved in the ideas and is not sure whether that is the correct method for solving such a problem.

I am not sure where does the (Z) value of (0) come from if we only have 2 dimensional point? +1 for the details.
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Emmad KareemNov 15 '11 at 9:25

@Emmad Kareem, it is a 2-d problem since x+15y+7z=44, which is a plane. The problem is reduced to a 2-d linear programming, but f change with 3-d point, (x,y,z). Am I make it clearer now?
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pureskyNov 15 '11 at 14:33